Abstract: Several ongoing research problems, on image processing of medical images and bio-mathematics, will be addressed. These are problems whose formulation and solution involve a broad range of interdisciplinary concepts as PDEs (partial differential equations), numerical analysis, optimization and scientific computing.Apart the scientific challenges, one of the main goals is to assist physicians with auxiliary screening/diagnosis/prognosis tools.The image processing problems refer to the in vivo detection of abnormalities/lesions in gastroenterological imagery, obtained with wireless endoscopic capsules. A short description of some mathematical techniques attempting to solve these problems will be considered.The bio-mathematics problems focus on in vivo physiologic parameter estimation. These are formulated as PDE-constrained optimization models. Some details on the mathematical approach for determining their solutions, which is based on Lagrange multiplier theory, will be given.The results achieved so far, for these particular image processing and bio-mathematics problems, will be shown and discussed.